Session S38 - Geometric Potential Analysis

Monday, July 19, 19:35 ~ 20:05 UTC-3

A Sharp Liouville Principle for $\Delta_m u+u^p|\nabla u|^q\leq 0$ on Geodesically Complete Noncompact Riemannian Manifolds

Yuhua Sun

Nankai University, China   -   sunyuhua@nankai.edu.cn

For $(m,p,q)\in (1,\infty)\times\mathbb R\times\mathbb R$, this paper establishes a sharp Liouville principle for the weak solutions to the quasilinear elliptic inequality of second order $\Delta_m u+u^p|\nabla u|^q\leq0$ on the geodesically complete noncompact Riemannian manifolds, which is novel even in the special case of Euclidean space.

Joint work with Jie Xiao (Memorial University of Newfoundland, Canada) and Fanheng Xu (Sun Yat-Sen University, China).

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